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Undergraduate Program in Mathematics

The four-year undergraduate program in mathematics leads to the degree of Bachelor of Science. The purpose of the undergraduate option is to give students an understanding of the broad outlines of modern mathematics, to stimulate their interest in research, and to prepare them for later work, either in pure mathematics or allied sciences. Unless students have done very well in mathematics courses in their freshman and sophomore years, they should not contemplate specializing in mathematics.

Since the more interesting academic and industrial positions open to mathematicians require training beyond a bachelor's degree, students who intend to make mathematics their profession must normally plan to continue with graduate study. Some students use their background in mathematics as an entry to other fields such as physics, computer science, statistics, economics, business, finance, medicine, or law.  

The schedule of courses in the undergraduate mathematics option is flexible. It enables students to adapt their programs to their needs and mathematical interests and gives them the opportunity of becoming familiar with creative mathematics early in their careers. In particular, students are encouraged to consider courses in areas such as applied and computational mathematics, physics, finance, economics, control and dynamical systems, computer science, electrical engineering, and computation and neural systems.

During each term of their junior and senior years, students normally take 18 units of courses in mathematics or applied and computational mathematics, including the required courses Ma 108abc and 109abc. Any course listed under applied and computational mathematics is regarded as an elective in mathematics and not as an elective in science, engineering, or humanities. Those who have not taken Ma 5 as sopohomores must do so as juniors. Overloads in course work are strongly discouraged; students are advised instead to deepen and supplement their course work by independent reading.

A student whose grade-point averages are less than 1.9 at the end of the academic year in the subjects under mathematics and applied and computational mathematics may, at the discretion of the department, be refused permission to continue the work in the mathematics option.


Option Requirements

  1. Ma 2
  2. Ma 3 or Ma 144a
  3. Either Ph 2bc or Ph 12abc (the departmental reccomendation is the Ph 12abc sequence).
  4. Ma 5abc, Ma 10, Ma 108abc, Ma 109abc.
  5. Ma/CS 6a or Ma 121a.
  6. Ma/CS 6c or Ma 116a or Ma/CS 117a.
  7. 45 additional units in Ma or ACM numbered 90 or above (other than Ma 98). Courses in other options with high mathematical content may be used to fulfill this requirement with the approval of the executive officer for mathematics. Of these 45 units at most 18 can be in ACM or other courses outside Ma.
  8. Math majors must take two quarters (18 units) of a single course, chosen from the mathematics course listings with numbers between 110 and 190, inclusive. (In years where one of these courses is given as a one-term course only, it cannot be used to satisfy this requirement.) These two quarters may be used to meet requirements 2, 4, or 5.
  9. Unlike courses satisfying requirements 5 and 6, which may be taken pass/fail, none of the courses satisfying requirements 1-4 may be taken on a pass/fail basis.
  10. Passing grades must be earned in a total of 486 units, including the courses listed above.

Note: Requirements 1 and 2 only apply to students who enter Caltech September 2013 or later.


Typical Course Schedule




Units per term



1st

2nd

3rd

Second Year

Ma 2ab
Linear Algebra, Statistics, and Differential Equations (4-0-5)

9

9

-
Ph 2ab
Statistical Physics, Waves, and Quantum Mechanics (4-0-5)

9

9

-
Ma 5abc
Introduction to Abstract Algebra (3-0-6)

9

9

9

Humanities

9

9

9

Electives*

9

9

27

Total

45

45

45

Third Year

Ma 10
Oral Presentation

3

-
-
Ma 108abc
Classical Analysis (3-0-6)

9

9

9
Ma/CS 6ac
Introduction to Discrete Mathematics (3-0-6)

9

-

9

Humanities Electives

9

9

9

Electives*

18

27

18

Total

48

45

45

Fourth Year

Ma 109abc
Introduction to Geometry and Topology (3-0-6)

9

9

9

Humanities Electives

9

9

9

Electives*

27

27

27

Total

45

45

45
* Includes menu course (2nd year, if not taken in freshman year). Also must include courses to meet items 4, 5 under option requirements.

 



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